ESE 102 Problem Set 1 Due Oct 15, 2012 at 5pm 1) Seawater density and water masses For this problem you will need to download the matlab scripts that calculate various physical properties of seawater. You can find them here:

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For this problem you will need to download the matlab scripts that calculate variousphysical properties of seawater. You can find them here:

http://www.cmar.csiro.au/datacentre/ext_docs/seawater.htm

You will notice that there is a large disclaimer at this site that says these scripts are out ofdate and that the salinity scale of seawater has now changed. This is all true, and you arewelcome to read about it all in depth, but for this problem I would like you to use the oldseawater equation of state (EOS-80). I have not vetted the new scripts for myself yet, soI am asking you to use the old ones. For bonus points you can do this problem with bothequations of state and compare the differences. You will also need the temperature andsalinity profile from the class web page titled, ‘CTDProfile_45S_145E.xls’.

First, calculate the potential temperature profile. Next compute the sigma-theta andsigma-2 profiles. What, if any, are the differences? What is the mixed layer depth? Arethere any water masses in this profile (it was taken just south of Tasmania in January2008.

2) The strontium cycle: a one-box model

(It might help to read: Richter and Turekian, EPSL 119:121(1993))

Sr is essentially conservative in seawater, with a concentration of 90 μmol / kg. Themajor Sr input is about 3.3× 1010

mol

/ year

from rivers, balanced by sedimentation incarbonates (hydrothermal cycling is of order 1× 1010

mol

/ year and ignored here).Geochemists are interested in it mostly because87Sr is producedby

the slow decay of87Rb, which concentrates in continental rocks, so that

changes in the seawater87Sr/86Srratio over long periods reflect the changing balance between river (continental) andhydrothermal (basalt) flow. Here, we will calculate the response time of the ocean87Sr/86Sr ratio to a change in the rate of river flow.

(a) What is the residence time of Sr in the ocean with respect to river input? Themass M of ocean water is 1.42× 1024

kg.

(b) Begin with a steady-state model ocean with a river input F0

balanced bysedimentation. Suppose that the river Sr input oscillates over some timescale, say becauseof climate, sea-level, or tectonic oscillations. Let the river input be a sine wave

F(t) = F0

+ A∙sin(2πt/τ)

(1)

where A is the oscillation amplitude and τ its timescale. Assuming that the removal of Srfrom the ocean is first-order in the Sr concentration, draw the relative fluctuation in oceanSr concentration for a given A for τ 5 times less then, about equal to, and 5 times greaterthan the residence time.

(c) Plot the amplitude of ocean Sr concentrations C(t)

and the phase shift betweenthe maximum in C(t) and the maximum in F(t) as a function of the oscillation timescale τ.

(d) River Sr has a mean87Sr/86Sr ratio of 0.711, compared with the modern oceanratio of 0.709 (the difference is thought to be due tohydrothermal exchange with basalt).Assuming that the river Sr isotopic composition remains the same and that sedimentationdoes not fractionate, what is the relative change A/F0

in the river Sr flux over glacial-interglacial time scales (τ =105

year) required for the ocean87Sr/86Sr ratio to oscillate by3 ×10−5

(close to the detection limit) over this timescale? Fluctuations of this magnitudehave been reported, though their interpretation remains controversial.

For (b-d), you will want to use a one-box ocean model, as sketched below.